Resolving Transition Paths from Single-Molecule FRET with Simulation-Based Inference

In single-molecule FRET (smFRET), two dyes attached to a biomolecule emit a stream of photons whose colors depend on the inter-dye distance. The photon stream is thus an indirect measurement of the molecule's conformational dynamics. We model the dynamics of the inter-dye distance as diffusion on a one-dimensional free-energy landscape $u(x)$ with diffusion coefficient $D$. Combined with a photon-emission model, this describes the smFRET experiment. The most informative parts of a trajectory are transition paths, the rare and brief events in which the system crosses between states. Under standard conditions, a single transition contributes only a handful of photons from the transition region, whereas dedicated experiments resolve individual transition paths with many photons. Because the likelihood of such transition paths is intractable, we analyze them with simulation-based inference (SBI). We augment the simulator to generate only smFRET transition paths, and neural posterior estimation aggregates many recorded transitions into a single amortized posterior over $u(x)$ and $D$. On synthetic photon streams, we recover the ground-truth landscapes and diffusion coefficients. We additionally apply our posterior to real experimental data, where it deviates from a previous analysis, potentially exposing model misspecification.